Question

The production function at Jerry’s Copy Shop is q=1000min(L,3K) , where q is the number of copies per hour, L is the number of workers, and K is the number of copy machines. Draw the following graphs. The graphs should have the number of workers, L, on the x-axis.

Draw the isoquants for this production function for q = 1000, 2000, and 3000. [4 pts.]

Draw the total product of labor (TP_L), average product of labor (AP_L), and marginal product of labor (MP_L) curves for this production function, assuming K = 1. [6 pts.]

Answer 1

a) Isoquants are drawn below. For q = 1000, we have 1000 = 1000min(L, 3K) implying min(L, 3K) = 1 for L = 3K, = 1

For q = 2000, we have 2000 = 1000min(L, 3K) implying min(L, 3K) = 2 for L = 3K = 2.

For q = 3000, we have 3000 = 1000min(L, 3K) implying min(L, 3K) = 3 for L = 3K = 3

b) The graph is provided below. For L = 0, 1 and 2, we see that output is q = 1000min(0, 3) or 0, q = 1000min(1, 3) = 1000 or q = 1000min(2, 3) = 2000. For L = 3, 4, and so on, q is fixed at 3000. APL = TPL/L and MPL is the difference of TPL for two labor units.

Labor	Output/TPL	MPL	APL
0	0
1	1000	1000	1000
2	2000	1000	1000
3	3000	1000	1000
4	3000	0	750
5	3000	0	600
6	3000	0	500
7	3000	0	428.6